The Associations between Ordinality and Mathematical Development Open Access

Abstract

In the modern world, mathematical competence is key to the competiveness of countries as well as individuals. Unfortunately, the mathematical abilities of American students lag significantly behind those of other industrialized nations (OECD, 2016). Thus, this dissertation was motivated by the broad goals of informing theoretical debates about the cognitive foundations of mathematics but also the practical importance of improving education in mathematics. Recent research suggests links between mathematical development and foundational abilities such as reasoning about ordinality. However, questions concerning the mechanisms underlying these links remain largely unresolved.

To answer these questions, this dissertation tested how a specific component of ordinality, namely rank, was related to early mathematical competence. In Paper 1, I present a study that tested the developmental relation between rank and exact number representations in 3- and 4-year-olds. Results showed that children who were better at tracking the rank of an item within a sequence also acquired more number words. Moreover, children who could reliably name the next number word in the count list also had a better grasp of numerical equality and a greater repertoire of number words. These findings suggest the ability to extract rank information from the count list is critical for the acquisition of number words and exact number representations. In Paper 2, I present a study that tested the developmental relation between rank-based operations and symbolic arithmetic. Results showed that children who were more proficient in making inferences based on inter-item distance between letters were better at solving symbolic arithmetic problems. Moreover, children who understood how rank should be updated after item insertion or removal also showed better arithmetic performance. The findings of Paper 2 suggest rank-based operations are recruited for the computation of addition and subtraction. Together, these two studies help to pinpoint the relations between specific ordinal abilities and early mathematical competence, which is critical for understanding the nature of the associations between ordinality and the development of mathematical competence.

Table of Contents

Table of Contents

1. Introduction

a. Different aspects of ordinality

b. The role of ordinality in mathematical development: state the of current literature

c. Overview of the dissertation

2. Paper 1: The first number is one: The associations between the ordinal concept of rank and cardinality

a. Abstract

b. Introduction

i. Ordinality as position

ii. How might ordinality contribute to representations of exact number?

iii. Current Study

c. Method

i. Participants

ii. Tasks and Procedure

d. Results

i. Preliminary analyses: Performance by Task

ii. Relations between Ordinality and Exact Number Representations

e. Discussion

f. References

3. Paper 2: The relation between ordinal concepts and children's arithmetic competence

a. Abstract

b. Introduction

i. Connection between Ordinality and Arithmetic

ii. Current Study

c. Method

i. Participants

ii. Tasks and Procedure

d. Results

i. Performance on Individual Measures

ii. Relations between arithmetic and ordinal abilities

iii. The relation between ANS acuity, ordinal abilities and arithmetic ability

e. Discussion

i. The development of rank-based abilities

ii. Relation between rank-based relations and symbolic arithmetic

iii. The role of ordinality in the causal pathway between ANS and symbolic arithmetic

f. References

4. Conclusions

i. Issue 1: Development of ordinality

ii. Issue 2: The specific contributions of ordinality to the understanding of
symbolic numbers

iii. Limitations and future research directions

5. References

About this Dissertation

Rights statement

• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Laney Graduate School
Department	Psychology
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Psychology, Developmental
Keyword	Numerical ability Exact Numbers Arithmetic Cardinality Principle Mathematical Development Order
Committee Chair / Thesis Advisor	Lourenco, Stella, Emory University
Committee Members	Rochat, Philippe, Emory University Hampton, Robert, Emory University Wolff, Phillip, Emory University Nygaard, Lynne, Emory University

Last modified

Primary PDF

Thumbnail	Title	Date Uploaded	Actions
	The Associations between Ordinality and Mathematical Development ()	2018-08-28 15:42:21 -0400	Press to Select an action Download

Supplemental Files

Thumbnail	Title	Date Uploaded	Actions